In figure, if ABDC and AC, PQ intersect each other at the point 0. Prove that 0A. CQ = OC.AP.


Given,

AC and PQ intersect each other at the point O and ABDC.


in ∆AOP and ∆COQ,


AOP = COQ [vertically opposite angles]


APO = CQO [since, ABDC and PQ is transversal, so alternate angles]


∆AOP ∆COQ [by AAA similarity criterion]


Then, OA/OC = AP/CQ


[since, corresponding sides are proportional]


OA × CQ = OC × AP


Hence Proved.


5
1